Finite Group Databasebeta

← #17993682

Subgroups — #17993682

Order 4736.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558186C211yesmaximal, characteristic, complemented
2#14557725C211yesmaximal, characteristic, complemented
3#14557725C211yesmaximal, characteristic, complemented
4#14557279C211yesmaximal, characteristic, complemented
5#14557262C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic, complemented
7C37×#486C211yesmaximal, characteristic, complemented
8C2×#10596966—21no—
9C2×#10596939—21no—
10C2×#10596939—21no—
11#11924521—22no—
12#11924512—21no—
13#11924511—21no—
14C4×D148C2211yescharacteristic
15C4×D148C2211yescharacteristic
16C4⋊C4×D37—21no—
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924457—21no—
20#11924457—21no—
21C4⋊Q8×C37C2211yescharacteristic
22#127×C37C2211yescharacteristic
23#102×C37—22no—
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29#10596966—42no—
30#10596966—42no—
31C2×D148—22no—
32C2×D148D411yescharacteristic
33C2×D148D411yescharacteristic
34C2×C4×D37—22no—
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C8×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37D412yes—
40C42×C37C2311yescharacteristic
41#10596939—42no—
42#10596939—42no—
43#10596938—22no—
44#10596938—21no—
45#10596938—21no—
46C4⋊Dic37D411yescharacteristic
47C4⋊Dic37D411yescharacteristic
48#10596936—22no—
49C2×#64436—21no—
50C2×#64436—21no—
51C23×C37—41no—
52C22×D37—21no—
53C22×D37—21no—
54Q8×C37—41no—
55Q8×C37—41no—
56D4×C37—42no—
57D4×C37—41no—
58D4×C37—41no—
59D4×C37—41no—
60D4×C37—41no—
61C2×C4×C37—22no—
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×Dic37—21no—
66C2×Dic37—21no—
67D148—21no—
68D148—21no—
69D148—21no—
70D148—44no—
71D148D812yescomplemented
72C4×D37—44no—
73C4×D37—41no—
74C4×D37—41no—
75C4×D37—41no—
76C4×D37—41no—
77C8×C37—41no—
78#64436—41no—
79#64436—41no—
80C22×C37—81no—
81C22×C37—81no—
82C22×C37—81no—
83C22×C37#12011yescharacteristic
84C2×D37—22no—
85C2×D37—41no—
86C2×D37—41no—
87C2×D37—41no—
88C2×D37—41no—
89C2×D37—41no—
90C4×C37—21no—
91C4×C37—42no—
92C4×C37C2×D811yescharacteristic
93C4×C37#13511yescharacteristic
94C4×C37AGL(1,ℤ/8)11yescharacteristic
95C4×C37AGL(1,ℤ/8)11yescharacteristic
96Dic37—41no—
97Dic37—41no—
98#1625—371nomaximal, Sylow
99C2×C37—161no—
100C2×C37#44711yescharacteristic
101C2×C37#44911yescharacteristic
102C2×C37#45411yescharacteristic
103D37—42no—
104D37—81no—
105#547—371no—
106#486D3711yescharacteristic, complemented
107#459—371no—
108#459—371no—
109#332—371no—
110D4⋊C8—371no—
111D4⋊C8—371no—
112C37#162511yescharacteristic, complemented, Sylow
113C2×#41—741no—
114C2×D8—741no—
115C2×D8—741no—
116C4⋊Q8C2×D3711yescharacteristic
117#127C2×D3711yescharacteristic
118#123—742no—
119C22⋊Q8—741no—
120#121—741no—
121C4×D4—371no—
122C4×D4—371no—
123C2×C4⋊C4—741no—
124C4⋊C8—371no—
125C4⋊C8—371no—
126#102—22no—
127#102—741no—
128#102—741no—
129C4×C8C2×D3711yescharacteristic
130#41—1482no—
131#41—1482no—
132C2×Q8—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—371no—
137C2×D4—371no—
138C2×D4—742no—
139C22×C4—742no—
140C22×C4—741no—
141C22×C4—741no—
142D8—1482no—
143D8—1482no—
144C2×C8—21no—
145C2×C8—741no—
146C2×C8—741no—
147C4⋊C4—21no—
148C4⋊C4—371no—
149C4⋊C4—371no—
150C4⋊C4—742no—
151C4⋊C4C22⋊D3712yes—
152C22⋊C4—742no—
153C22⋊C4—741no—
154C22⋊C4—741no—
155C42C22×D3711yescharacteristic
156C23—41no—
157C23—741no—
158C23—741no—
159Q8—41no—
160Q8—41no—
161D4—42no—
162D4—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—372no—
167D4—741no—
168D4—741no—
169D4—741no—
170D4—1484no—
171C2×C4—22no—
172C2×C4—741no—
173C2×C4—741no—
174C2×C4—1484no—
175C2×C4—1481no—
176C2×C4—1481no—
177C2×C4—1481no—
178C2×C4—1481no—
179C2×C4D4×D3711yescharacteristic
180C2×C4D4×D3711yescharacteristic
181C2×C4C2×C22⋊D3711yescharacteristic
182C8—41no—
183C8—1481no—
184C8—1481no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—742no—
189C22—1481no—
190C22—1481no—
191C22—1481no—
192C22—1481no—
193C22—1481no—
194C22#1192450411yescharacteristic
195C4—21no—
196C4—42no—
197C4—1481no—
198C4—1481no—
199C4D8×D3711yescharacteristic
200C4#1192455711yescharacteristic
201C4#1192456011yescharacteristic
202C4#1192456311yescharacteristic
203C2—161no—
204C2—2961no—
205C2—1482no—
206C2#1455766511yescharacteristic
207C2#1455767711yescharacteristic
208C2#1455770511yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#486C2
socleC22×C37#120
hypercenter#486D37
hypocenterC37#1625
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14558186C2semidirect
2. #14557725C2semidirect
3. #14557725C2semidirect
4. #14557279C2semidirect
5. #14557262C2semidirect
6. #14557262C2semidirect
7. C37×#486C2semidirect
71. D148D8semidirect
106. #486D37semidirect
112. C37#1625semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145581862
#145577252
#145572792
#145572622
C37×#4862
#162537